# Angular Momentum

## Key Questions

see below

#### Explanation:

For linear motion we have the conservation of linear momentum(mass $\times$linear velocity): that is in any system, providing no external forces act, the total linear momentum is always constant.

For rotational bodies we have another conservation law. Providing NO external Torques act, the total angular momentum
(moment of inertia $\times$ angular velocity) is constant.

Angular momentum is the rotational analogue of the Linear momentum.

#### Explanation:

Angular momentum is denoted by $\vec{L}$.

Definition :-

The instantaneous angular momentum $\vec{L}$ of the particle relative to the origin $O$ is defined as the cross product of the particle’s instantaneous position vector $\vec{r}$and its instantaneous linear momentum $\vec{p}$

$\vec{L}$= $\vec{r}$$\times$$\vec{p}$

For a rigid body having fixed axis rotation , the angular momentum is given as $\vec{L} = I \vec{\omega}$ ; where $I$ is the Moment of Inertia of the body about the axis of rotation.

The net torque $\vec{\tau}$ acting on a body is give as the rate of change of Angular Momentum.

$\therefore \sum \vec{\tau} = \frac{\mathrm{dv} e c L}{\mathrm{dt}}$